Definition:Limit of Sequence/P-adic Numbers

Definition

Let $p$ be a prime number.

Let $\struct {\Q_p, \norm {\, \cdot \,}_p}$ be the $p$-adic numbers.

Let $\sequence {x_n} $ be a sequence in $\Q_p$.

Let $\sequence {x_n}$ converge to $x \in \Q_p$

Then $x$ is a limit of $\sequence {x_n}$ as $n$ tends to infinity which is usually written:

$\ds x = \lim_{n \mathop \to \infty} x_n$

Also see

• Convergent Sequence in P-adic Numbers has Unique Limit